A Primal-dual Forward-backward Splitting Method for Cross-diffusion Gradient Flows with General Mobility Matrices

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Hauptverfasser: Deng, Yunhong, Wei, Chaozhen
Format: Preprint
Veröffentlicht: 2025
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author Deng, Yunhong
Wei, Chaozhen
author_facet Deng, Yunhong
Wei, Chaozhen
contents In this work, we construct a primal-dual forward-backward (PDFB) splitting method for computing a class of cross-diffusion systems that can be formulated as gradient flows under transport distances induced by matrix mobilities. By leveraging their gradient flow structure, we use minimizing movements as the variational formulation and compute these cross-diffusion systems by solving the minimizing movements as optimization problems at the fully discrete level. Our strategy to solve the optimization problems is the PDFB splitting method outlined in our previous work \cite{PDFB2024}. The efficiency of the proposed PDFB splitting method is demonstrated on several challenging cross-diffusion equations from the literature.
format Preprint
id arxiv_https___arxiv_org_abs_2510_27660
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Primal-dual Forward-backward Splitting Method for Cross-diffusion Gradient Flows with General Mobility Matrices
Deng, Yunhong
Wei, Chaozhen
Numerical Analysis
Optimization and Control
In this work, we construct a primal-dual forward-backward (PDFB) splitting method for computing a class of cross-diffusion systems that can be formulated as gradient flows under transport distances induced by matrix mobilities. By leveraging their gradient flow structure, we use minimizing movements as the variational formulation and compute these cross-diffusion systems by solving the minimizing movements as optimization problems at the fully discrete level. Our strategy to solve the optimization problems is the PDFB splitting method outlined in our previous work \cite{PDFB2024}. The efficiency of the proposed PDFB splitting method is demonstrated on several challenging cross-diffusion equations from the literature.
title A Primal-dual Forward-backward Splitting Method for Cross-diffusion Gradient Flows with General Mobility Matrices
topic Numerical Analysis
Optimization and Control
url https://arxiv.org/abs/2510.27660